What you are feeling sounds similar to the kind of sensation most people feel when they are on a rollercoaster. It may just be that you are not used to the weightless feeling of accelerating downhill, or you might be more sensitive to it than most people.
If you know the hill is coming and you know you are going to hate it, this alone can be enough to make you tense up. In your position I would attempt to look at the road as normal throughout all the downhill parts of your journey. Know the hill is approaching and, instead of bracing yourself, relax and accept it and don't resort to looking at the floor! It might help to try not even to move a muscle. Also, it is often recommended in times of tension to take some deep breaths.